My bonneville has air suspension like many of them. Today I had the linkage installed that adjusts the shocks. I noticed however that the air compressor comes on after the car shuts off and stays on for 4-5 minutes! Is this normal or is there a problem with my air suspension? If there is a problem, I am thinking that the previous owner may have removed the linkage to solve it.

The air compressor also comes on if you turn it on in the trunk. The inflator does have pressure too, I assume that it uses the same line as the shocks, right?

It'* running too long, then the timer is kicking in and shutting it off. Likely, you have a leak in the system, so that the struts are not raising the car. Check the tubes that go from the air compressor to the struts in the back.